Final answer:
The least influential factor in how nations formed alliances during European wars was likely the number of battles fought. Historical alliances were more deeply influenced by religious affiliations, family ties, and the outcomes of earlier conflicts.
Step-by-step explanation:
When taking sides in European wars, the factor that would have least influenced how nations formed alliances is likely to be C. The number of battles fought. The other factors listed, such as the religions of the countries involved (A), family ties among the countries (B), and the outcomes of earlier wars (D), have historically played significant roles in alliance formations. For example, religious affinities could unite countries with shared beliefs and lead to diplomatic support or military alliances, like those seen during the Protestant Reformation or the Thirty Years War. Similarly, family ties among European royalty often influenced alliances, with kinship networks extending across national borders, while the outcomes of earlier wars affected future treaties and alliances based on shifts in power or attempts at revenge. In contrast, the mere number of battles fought would be too simplistic to strongly influence complex alliance systems, as the motivations behind wars and the strategic interests of the countries were far more crucial in alliance decisions.